Post two examples that are similar to questions to the following photo. Include the question and your solution. Example 1: Relates to converting between radians and degrees Example 2: Use the relationship a=rθ to solve for either the arc length (a), the radius (r) or the angle in radians (θ).
Answers
1) Given the angles below transform into degrees or radians as needed, round to two decimal points if necessary.
\(\begin{gathered} 4\pi \\ 720\degree \\ 10\degree \\ \frac{5}{8}\pi \end{gathered}\)In general, 2pi=360°; then, 4pi radians refer to 2 revolutions around a circumference, as shown in the diagram below
Therefore, 4pi=0°=360°.
Similarly,
\(\begin{gathered} \frac{360\degree}{2\pi}=\frac{720\degree}{x} \\ \Rightarrow x=2\pi(\frac{720}{360})=2\pi *2=4\pi=0 \end{gathered}\)720°=0 radians
\(\begin{gathered} \frac{2\pi}{360\degree}=\frac{x}{10\degree} \\ \Rightarrow x=2\pi(\frac{10}{360})=\frac{\pi}{18} \end{gathered}\)10°=pi/18 radians.
\(\begin{gathered} \frac{x}{\frac{5}{8}\pi}=\frac{360\degree}{2\pi} \\ \Rightarrow x=360\degree(\frac{\frac{5}{8}\pi}{2\pi})=360\degree(\frac{5}{16})=112.5 \end{gathered}\)5pi/8=112.5°.
2) Given that the area of a circle is 30pi and an arc length on it is pi/2; find the central angle generated by such arc in radians, round to three decimal places if needed.
The area of a circle is given by
\(\begin{gathered} A=\pi r^2 \\ r\rightarrow radius \end{gathered}\)Then, in our case,
\(30\pi=r^2\pi\Rightarrow r=\sqrt{30}\)On the other hand, an arc length is given by the formula below
\(arc=r\theta\)In our case,
\(\begin{gathered} arc=\frac{\pi}{2} \\ \Rightarrow\frac{\pi}{2}=\sqrt{30}\theta \\ \Rightarrow\theta=\frac{\pi}{2\sqrt{30}} \\ \Rightarrow\theta\approx0.287\text{ radians} \end{gathered}\)The answer is 0.287 radians.
Related Questions
Sierra says that she can simplify the left side of the inequality shown by combining the terms within the parentheses but that she can't do the same thing on the right side. Is Sierra correct? Explain.
4(-4 + 9) + 1 ≥ -2(y + 7) - 8
Answers
Answer: Yes, Sierra is correct.
Step-By-Step Explanation:
The parenthesis on the left side is (-4+9). This can be combined because both terms are two constants. Constants are any terms in a algebraic equation or inequality whose value does not changed and is pre-defined. In this parenthesis, the answer would be 5.
The parenthesis on the right side contains one constant (7) and one variable (y). Since you can only combine like terms, y and 7 cannot be combined. Therefore, you cannot combine the right-side parenthesis.
So, Sierra is correct
URGERNT!!!PLS AT LEAST TAKE A LOOK!!! SHARE YO SMARTNESSS!! AND BLESS YOUR GRADES!
Which sign explains the relationship between m∠1 and m∠2 in the diagram?
A) not equal to
B) >
C) <
D) =
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Answer:
Dear Laura Ramirez
Answer to your query is provided below
Option D is correct.
Reason - Because of Hinge and Converse of Hinge theorem
1⁄2 · n = 3 I don't know what to do
Answers
Answer:
n=6
Step-by-step explanation:
\(\frac{1}{2} n=3\)
Multiply both sides by 2
2*1/2n=3*2
Simplify;
n=6
Answer: n=6
Step-by-step explanation:
6*1/2=3 so this is y n=6.
NO LINKS!! URGENT HELP PLEASE!!!
11. Write the equation for the graph
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This is the same as writing y = sqrt(4(x+5)) - 1
===============================================
Explanation:
The given graph appears to be a square root function.
The marked points on the curve are:
(-4,1)(-1,3)(4,5)Reflect those points over the line y = x. This will have us swap the x and y coordinates.
(-4,1) becomes (1,-4)(-1,3) becomes (3,-1)(4,5) becomes (5,4)Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.
----------
Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).
Plug the coordinates of each point into the template y = ax^2+bx+c.
For instance, plug in x = 1 and y = -4 to get...
y = ax^2+bx+c
-4 = a*1^2+b*1+c
-4 = a+b+c
Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c
Repeat for (5,4) and you should get 4 = 25a+5b+c
We have this system of equations
-4 = a+b+c-1 = 9a+3b+c4 = 25a+5b+cUse substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.
In other words
a = 1/4, b = 1/2, c = -19/4
We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4
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Next we complete the square
y = (1/4)x^2+(1/2)x-19/4
y = (1/4)( x^2+2x )-19/4
y = (1/4)( x^2+2x+0 )-19/4
y = (1/4)( x^2+2x+1-1 )-19/4
y = (1/4)( (x^2+2x+1)-1 )-19/4
y = (1/4)( (x+1)^2-1 )-19/4
y = (1/4)(x+1)^2- 1/4 - 19/4
y = (1/4)(x+1)^2 + (-1-19)/4
y = (1/4)(x+1)^2 - 20/4
y = (1/4)(x+1)^2 - 5
The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.
----------
The last batch of steps is to find the inverse.
Swap x and y. Then solve for y.
y = (1/4)(x+1)^2 - 5
x = (1/4)(y+1)^2 - 5
x+5 = (1/4)(y+1)^2
(1/4)(y+1)^2 = x+5
(y+1)^2 = 4(x+5)
y+1 = sqrt(4(x+5))
y = sqrt(4(x+5)) - 1
I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.
You can also use a tool like GeoGebra to verify the answer.
A human hair was measured to be 8.0•10-4 inch thick. A cat hair is measured to be 4.0•10^-1. How much greater is the thickness of the cat hair than the human hair? Writ this in standard form.
Whoever gets this right I will mark brainiest and 60 points!!
Answers
Answer:
500 times
Step-by-step explanation:
Divide the thickness of a cat hair by the thickness of a human hair.
4.0 × 10^-1 / 8.0 × 10^-4 =
= 0.5 × 10^3
= 500
500 times
Lorelei tosses a coin 4 times. What is the probability of tossing four heads? Express as a percent. Round to the nearest tenth if necessary.
Answers
Answer:
6.2%
Step-by-step explanation:
For each time the coin is tossed, there are only two possible outcomes. Either it is heads, or it is not. The probability of a toss resulting in heads is independent of other tosses. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
Fair coin:
Equally as likely to be heads or tails, so \(p = 0.5\)
Lorelei tosses a coin 4 times.
This means that \(n = 4\).
What is the probability of tossing four heads?
This is P(X = 4).
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 4) = C_{4,4}.(0.5)^{4}.(0.5)^{0} = 0.062\)
0.062 = 6.2% probability of tossing four heads
jared buts 2.4 pounds of broccoli for $3.24 which equation could jared use to find c, the cost of each pound of broccoli
Answers
Answer:
2.4c = 3.24
Step-by-step explanation:
Answer:
it is 4 ounces + 18 ounces
ZA and B are supplementary
mZA= 2n and mZB = 3n + 20
Find mZB
Am B = 12
B) mzB = 62
m B= 116
Dm B = 148
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Answer:
< A+< B =180
2n + 3n +20 =180
5n = 160
n = 32
(B= 116 ..........
answer is C
A student wants to earn a C for a class. To get this grade, the average of his six test scores must be 70.
He has the following grades on five tests:
60,78,65,68,72
What grade must the student get on the next test so that the average of his scores is 70?
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Answer: To find out what grade the student must get on the next test, we can use the following formula:
(current total of scores + desired score) / (total number of scores) = desired average
We know that the student's current total of scores is 60 + 78 + 65 + 68 + 72 = 363, and the desired average is 70. We also know that the student has taken five tests, so there is one test remaining.
Therefore, we can plug in these values into the formula:
(363 + x) / 6 = 70
Where x is the grade the student must get on the next test.
We can solve for x by multiplying both sides of the equation by 6:
363 + x = 420
x = 57
Therefore, the student must get a grade of 57 on the next test in order to have an average of 70.
Step-by-step explanation:
25.4 centimeters per second = 10 inches per second.
Hint: there are 2.54 centimeters in 1 inch.
true or false ?
Answers
Answer:
True
Step-by-step explanation:
2.54 centimeters = 1 inch
1 x 10 = 10 inches
2.54 x 10 = 25.4 centimeters
Good luck mate :)
PLEASE HELP - WORTH 70 POINTS! WILL GIVE BRAINLEST
Answers
The probability of rolling an odd product is 3/4 or 0.75.
The probability of rolling a product that is greater than or equal to 20 is 8/16 or 0.5.
The probability of rolling a product that is less than 10 is 1/4 or 0.25.
The probability of rolling a product that is a multiple of 10 is 3/16 or 0.1875.
What is probability?Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.
The probability of rolling an odd product is 3/4 or 0.75. This is because there are 12 odd products on the grid out of a total of 16 products.
The probability of rolling a product that is greater than or equal to 20 is 8/16 or 0.5. This is because there are 8 products on the grid that are greater than or equal to 20 out of a total of 16 products.
The probability of rolling a product that is less than 10 is 1/4 or 0.25. This is because there are 4 products on the grid that are less than 10 out of a total of 16 products.
The probability of rolling a product that is a multiple of 10 is 3/16 or 0.1875. This is because there are 3 products on the grid that are a multiple of 10 out of a total of 16 products.
Krystal's game is an example of probability. In this case, Krystal is using the grid to calculate the probability of different outcomes when rolling the two number cubes. By understanding the probability of different outcomes, Krystal can make informed decisions and predict the likely outcome of her game.
For more questions related to outcomes
https://brainly.com/question/25688842
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Pete asks Buzz for a truss with angles of 60°, 90°, and 30°. (He does not give side lengths.)
Is this enough information for Buzz to make a truss with the correct size and shape?
Explain.
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Simon pays $9 for 6 visits to swim at the community pool. He pays $18 for 12 visits to swim. How much does it cost for each visit to the pool?
Answers
Answer:
$1.50
Step-by-step explanation:
If you do cost per quantity you would get $9 over 6 visits. Then you divide both sides by 6 because to get to one by 6 it's 6 so when you divide both sides by 6 you would get 1.5 over 1 and all you do is add a zero because you're dealing with money
Hope this helps :)
Complete both transformations below.
Then enter the final coordinates of the figure.
A(-1,3)
B(2,1)
C(1-1)
1) <2,3>
2) Dilate K = 2
A" ([?], [])
B" ([][])
C" ([],[])
Enter
Answers
Answer:
A" (2, 12)
B" (8,8)
C" (6, 4)
Step-by-step explanation:
For each point P(x, y) of the image, the translations are as follows:
Translate P(x, y) by <2, 3> \(\longrightarrow\) P'(x + 2, y + 3) \(\longrightarrow\) P'(x', y')
Dilate P'(x', y') by 2 \(\longrightarrow\) P'' (x'', y'') \(\longrightarrow\) P(2x', 2y')
Point \(\longrightarrow\) Translate <2, 3> \(\longrightarrow\) Dilate by 2
A(-1, 3) \(\longrightarrow\) A'(-1 +2, 3 + 3) => A'(1, 6) \(\longrightarrow\) A''(2, 12)
B(2, 1) \(\longrightarrow\) B'(2 + 2, 1 + 3) => B'(4, 4) \(\longrightarrow\) B"(8, 8)
C(1, -1) \(\longrightarrow\) C'(1 + 2, -1 + 3) => C'(3, 2) \(\longrightarrow\) C"(6, 4)
Solve for x.
3х/6 + 1 = 7
x=4
x=12
x=16
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Hope this helps
Mr. Silvano drove 128.6 km each day for 8 days. Then, he drove 44.3 km each day for 12 days. What was the total distance Mr. Silvano drove?
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Answer:
Ans: 1559.6km
Step-by-step explanation:
(128.6x8)+(44.3x12)=1559.6km
Answer:1559.6km
Step-by-step explanation:
128.6*8=1,028.8
44.3*12=531.6
1,028+531.6=1559.6km
Let p=5-2i and q=-3+7i. Write the expression in the form a+bi:
pq
Answers
Answer:
Step-by-step explanation:
pq = (5-2i)×(-3+7i) = -15 + 35i +6i -14i^2
= -15 +41i -14(-1)
= -15 +41i +14 = -1+41i
Anyone got me with this I’ll cash app you
Answers
Answer:
0
Step-by-step explanation:
Since given line is parallel to x axis, so it's slope is zero.
Another way:
Line is passing through the points (2, - 1) & (3, - 1)
So,
\( slope=\frac{-1-(-1)}{3-2}\)
\( slope=\frac{-1+1}{1}\)
\( slope=\frac{0}{1}\)
\( slope=0\)
What is the amount earned by a car salesman if he sold a truck for $37.500 at a 2% commission? 15
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Find the exact value under the given conditions.
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I think is B
An IAS question. Add 10 and 4 and you get 2. how
Answers
Answer:
you make them into groups
Step-by-step explanation:
Answer:
Make them into groups
Step-by-step explanation:
Hope this helped have an amazing day!
Two sides of a triangle have the same length. The third side measures 3 m less than twice that length. The perimeter of the triangle is 25m. Find the lengths of the three sides.
Answers
Answer:
two sides have the length of 7m
third side is 11m
Step-by-step explanation:
perimeter is the sum of all sides
let 'n' = length of congruent sides
let '2n - 3' = length of third side
25 = n + n + 2n - 3
25 = 4n - 3
28 = 4n
n = 7m
2(7) - 3 = 11m
Enter the number that belongs in the green box
Answers
The number that belongs in the green box using sine rule is 13.96.
What is sine rule?The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
To calculate the number that belongs in the green box, we use the formula below
Formula:
SinA/a = SinB/b.................. Equation 1From the diagram,
Given:
A = 70°B = 61°b = 15a = xSubstitute these values into equation 1
Sin70°/15 = sin61°/xSolve for x
x = (15×sin61°)/sin70°x = 13.96Learn more about sine rule here: https://brainly.com/question/28523617
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What is the distributive property of 35y + 49
Answers
Answer:
7(5y+7)
Step-by-step explanation:
7×5y=35y
7×7=49
so its 7(5y+7)
Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves y = (x - 2)^4 and 8x - y =16 about the line x= 10?
A. Pi integral^4_2 {[10 - (1/8 y + 2)^2] - [10 - (2 + ^4 squareroot y)^2]} dy
B. Pi integral^16_0 {[10 - (1/8 y + 2)] - [10 - (2 + ^4 Squareroot)]}^2 dy
C. Pi integral^4_2 {[10 - (1/8 y + 2)] - [10 - 2 + ^4 squareroot y)]}^2 dy
D.Pi integral^16_0 {[10 - (1/8 y + 2)]^2 - [10 - 2 + ^4 squareroot y)]^2} dy
E. Pi integral^16_0 {[10 - (1/8 y + 2)^2] - [10 - 2 + ^4 squareroot y)^2]} dy
F. Pi integral^4_2 {[10 - (1/8 y + 2)]^2 - [10 - 2 + ^4 squareroot y)]^2} dy
Answers
Answer:
\(\displaystyle V = \pi \int _0^{16}\left[10-\left(\frac{1}{8}y-2\right)\right] ^2 - \left[10 - \left(2+y^{{}^{1}\!/\!{}_{4}}\right)\right]^2\, dy\)
Step-by-step explanation:
We want to find the volume of the solid obtained by rotating the region between the two curves:
\(y=(x-2)^4\text{ and } 8x-y=16\)
About the line x = 16.
Since our axis of revolution is vertical, we can use the washer method in terms of y.
\(\displaystyle V = \pi \int _c^d[R(y)]^2 -[r(y)}]^2\, dy\)
Where R(y) is the outer radius and r(y) is the inner radius.
First, solve each equation in terms of y:
\(\displaystyle x_1 = \frac{1}{8}y+2\text{ and } x_2 = y^{{}^{1}\! /\! {}_{4}}+2\)
From the diagram below, we can see that the outer radius R(y) is (10 - x₁) and that the inner radius r(y) is (10 - x₂). The limits of integration will be from y = 0 to y = 16. Substitute:
\(\displaystyle V = \pi \int_0^{16}\left[\underbrace{10-\left(\frac{1}{8}y+2\right)}_{R(y)}\right]^2 - \left[\underbrace{10-\left(y^{{}^{1}\!/\!{}_{4}}+2\right)}_{r(y)}\right]^2\, dy\)
Thus, our volume is:
\(\displaystyle V = \pi \int _0^{16}\left[10-\left(\frac{1}{8}y-2\right)\right] ^2 - \left[10 - \left(2+y^{{}^{1}\!/\!{}_{4}}\right)\right]^2\, dy\)
*I labeled the diagram incorrectly. Let R(x) be R(y) and r(x) be r(y).
What is the slope of a line that is perpendicular to the line with equation 12x+3y=9?
Answers
Answer:
The slope would be 1/4.
Step-by-step explanation:
To find the perpendicular slope first you have to set this equation to y
to do this you use the subtraction prop of equality and you will get 12x-9= -3y
then you divide by -3 on both sides to get y by itself
you will get -4x+3=y
now that you know the slope is -4, you must find the negative reciprocal slope of this which means you have to flip the numerator and denominator and make the sign its opposite.
The perpendicular slope would then be 1/4.
2/8x+3/8(x-1)=4 solve for x
Answers
\(\dfrac 28 x + \dfrac 38 (x-1) = 4\\\\\implies \dfrac 18(2x + 3x -3) = 4\\\\\implies 5x -3 = 32\\\\\implies 5x = 32 +3 \\\\\implies 5x = 35\\\\\implies x = \dfrac{35}5\\\\\implies x = 7\)
Answer:
The value of x is 7.
Step-by-step explanation:
Question :
\({\implies{\sf{\dfrac{2}{8} x + \dfrac{3}{8}(x - 1) = 4}}}\)
Solution :
\({\implies{\sf{\dfrac{2}{8} x + \dfrac{3}{8}(x - 1) = 4}}}\)
\({\implies{\sf{\dfrac{2}{8} \times x + \dfrac{3}{8}(x - 1) = 4}}}\)
\({\implies{\sf{\dfrac{2 \times x}{8} + \dfrac{3(x - 1)}{8} = 4}}}\)
\({\implies{\sf{\dfrac{2x}{8} + \dfrac{3x - 3}{8} = 4}}}\)
\({\implies{\sf{\dfrac{2x + 3x - 3}{8} = 4}}}\)
\({\implies{\sf{\dfrac{5x - 3}{8} = 4}}}\)
\({\implies{\sf{{5x - 3} = 4 \times 8}}}\)
\({\implies{\sf{{5x - 3} =32}}}\)
\({\implies{\sf{5x = 32 + 3}}}\)
\({\implies{\sf{5x = 35}}}\)
\({\implies{\sf{x = 35 \div 5}}}\)
\({\implies{\sf{x = \dfrac{35}{5}}}}\)
\({\implies{\sf{x = \cancel{\dfrac{35}{5}}}}}\)
\({\implies{\sf{x = 7}}}\)
\(\star{\underline{\boxed{\sf{\pink{x = 7}}}}}\)
Hence, the value of x is 7.
\(\rule{300}{1.5}\)
A car is 35.3m down the road from the lizard driving toward it at a speed of 30.5 m/s. How long will it take the car to drive 35.3 m? Round to a tenth of a second.
Answers
We need to find the time that the car takes to travel 35.3m if it is being driven at 30.5m/s.
Let's remember how velocity is definded:
\(V=\frac{\Delta x}{\Delta t}\)Where ∆x is the distance traveled, ∆t is the time taken to travel that distance, and V is the velocity. For this case we know velocity (V = 30.5 m/s) and the distance (∆x = 35.3 m). We need to find ∆t. Let´s replace values in the equation:
\(30.5m/s=\frac{35.3m}{\Delta t}\)We just need to solbe for ∆t:
\(\Delta t=\frac{35.3m}{30.5m/s}\approx1.1574s\)The car takes approximately 1.2 seconds (rounded to the nearest tenth of a second) to travel that distance.
Now, to know if the lizard will make it to the other side before the car gets there, we need to calculate the time the lizard takes to cross the road. We calculate it following the sae process we used for the car. For this case V = 2.8m/s and ∆x = 3 m. The lizard needs to cross the road in 1.2 seconds or less. Let's see:
\(2.8m/s=\frac{3m}{\Delta t}\)\(\Delta t=\frac{3m}{2.8m/s}\approx1.071s\)The lizard corsses the road in 1.1 seconds (rounded to the nearest tenth of a second). He takes less time than te car, hence, the lizard will be able to cross the road before the car gets there.
PLEASE HELP! I ONLY HAVE 8 MINUTES LEFT!
Answers
Brian has reduced his cholesterol level by 14% after his last check up. If his original level was 320, what is his approximate cholesterol level now? OA. 45 OB. 275 OC. 365 OD. 316
Answers
Let:
X = Original level of cholesterol
Xr = Reduced cholesterol
a = Amount of cholesterol reduced
so:
\(\begin{gathered} Xr=X-a \\ where\colon \\ X=320 \\ a=320\cdot(\frac{14}{100})=44.8 \\ so\colon \\ Xr=320-44.8 \\ Xr=275.2\approx275 \end{gathered}\)